Quadrilateral PQRS is inscribed in circle O . Opposite angles P and R measure (x+16)° and (6x−4)° , respectively. Determine the measure of the smaller angle.(1 point)

Question

Responses

56°
56°

40°
40°

24°
24°

20°

Answer 1

24°

To find the measure of the smaller angle, we can use the fact that opposite angles in an inscribed quadrilateral are supplementary.

So, (x+16)° + (6x-4)° = 180°
x + 16 + 6x - 4 = 180
7x + 12 = 180
7x = 168
x = 24

Now, we can substitute x back into the equation to find the measure of the smaller angle:
x + 16 = 24 + 16 = 40°

Therefore, the measure of the smaller angle is 40°.